/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
            if(false(),x,y) -> 0()
            if(true(),x,y) -> s(minus(x,y))
            if1(false(),x,y) -> mod(minus(x,y),y)
            if1(true(),x,y) -> x
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            minus(0(),y) -> 0()
            minus(s(x),y) -> if(gt(s(x),y),x,y)
            mod(x,0()) -> 0()
            mod(x,s(y)) -> if1(lt(x,s(y)),x,s(y))
        - Signature:
            {gt/2,if/3,if1/3,lt/2,minus/2,mod/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {gt,if,if1,lt,minus,mod} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
            if(false(),x,y) -> 0()
            if(true(),x,y) -> s(minus(x,y))
            if1(false(),x,y) -> mod(minus(x,y),y)
            if1(true(),x,y) -> x
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            minus(0(),y) -> 0()
            minus(s(x),y) -> if(gt(s(x),y),x,y)
            mod(x,0()) -> 0()
            mod(x,s(y)) -> if1(lt(x,s(y)),x,s(y))
        - Signature:
            {gt/2,if/3,if1/3,lt/2,minus/2,mod/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {gt,if,if1,lt,minus,mod} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
            if(false(),x,y) -> 0()
            if(true(),x,y) -> s(minus(x,y))
            if1(false(),x,y) -> mod(minus(x,y),y)
            if1(true(),x,y) -> x
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            minus(0(),y) -> 0()
            minus(s(x),y) -> if(gt(s(x),y),x,y)
            mod(x,0()) -> 0()
            mod(x,s(y)) -> if1(lt(x,s(y)),x,s(y))
        - Signature:
            {gt/2,if/3,if1/3,lt/2,minus/2,mod/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {gt,if,if1,lt,minus,mod} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          gt(x,y){x -> s(x),y -> s(y)} =
            gt(s(x),s(y)) ->^+ gt(x,y)
              = C[gt(x,y) = gt(x,y){}]

WORST_CASE(Omega(n^1),?)